Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
lengthT175 °C105 °C40 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 105 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 105 °CTc: 30 → 40 °C
ΔTlm = K
2.Easy
lengthT115 °C60 °C50 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 60 °C while the cold fluid heats from 20 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 60 °CTc: 20 → 50 °C
ΔTlm = K
3.Medium
lengthT140 °C30 °C125 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 30 to 125 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 125 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT100 °C50 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 480 kW. The hot fluid cools from 100 to 50 °C and the cold fluid heats from 10 to 80 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 480 kWU = 1000 W/(m²·K)Th: 100 → 50 °CTc: 10 → 80 °C
A = m²
5.Hard
lengthT80 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 80 °C and the cold stream at 10 °C. The exchanger has A = 1 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 80 °CTc,in = 10 °CA = 1 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT90 °C60 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 90 to 60 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 25 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.5 kJ/(kg·K)Th: 90 → 60 °Cṁc = 0.5 kg/sTc,in = 25 °CD = 25 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 102.1 K
  2. 2. ΔTlm = 51.49 K
  3. 3. A = 8.328 m²
  4. 4. A = 16.64 m²
  5. 5. Th,out = 62.5 °C
  6. 6. L = 101.3 m

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